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• explain a forward rate and calculate spot rates from forward rates, forward rates from spot rates, and the value of a bond using forward rates
• explain the effect of volatility on the arbitrage-free value of an option
• explain the use of interest rate swaps and options to alter portfolio cash flows and exposure to interest rate risk.
Question 1
Shares of Comfortably Numb plc (CN) are currently trading at $8.50. You want to insure your portfolio of CN shares against losses and consider using stock options that are valued with the help of the binomial model. In any year, the stock will either increase in value by 12% or fall in value by 12% per annum. The annual risk-free interest rate is 1.75%. No dividends are paid by CN.
• a.Construct a one-period binomial tree for the value of CN shares.
(3 marks)
• b.Calculate the value of a European call option on one CN share with an exercise price of £8.90 using the one-period binomial tree.
(8 marks)
• c.Is this European call in the money, at the money or out of the money? Justify your answer.
(2 marks)
• d.Calculate the value of a European put option on the CN share with an exercise price of £9.50.
(6 marks)
• e.Construct a two-period binomial tree (that is, covering two years) for the value of CN shares.
(2 marks)
• f.Calculate the value of a European call option on one CN share with an exercise price of £8.90 using the two-period binomial tree.
(5 marks)
• g.Why is the price in the two-period model in (f) different from the one in the one-period model in (b)?
(4 marks)
• h.What considerations should there be when deciding which options to use to insure a portfolio of CN shares against losses? (No calculations are needed here.)
(5 marks)
(Total: 35 marks)
Question 2
• a.In what sense do hedge funds ‘hedge’? In your answer, provide a definition of ‘hedging’, make reference to relevant strategies followed by hedge funds, and illustrate with real world examples.
(18 marks)
• b.Compare and contrast the typical approaches to investment followed by hedge funds and those followed by mutual funds.
(12 marks)
• c.Under what circumstances can hedge funds consistently generate a positive ‘alpha’ for investors? You might find it appropriate for your answer to be related to ideas of efficient markets.
(10 marks)
(Total: 40 marks)
Question 3
A client has a traditional portfolio comprising bonds and equities. She is considering moving some of her investments into alternative assets. However, she is unsure what is meant by ‘alternative assets’ and what are the particular features of this investment class.